Threshold and beyond: modeling the intensity dependence of auditory responses

Nonlinear cortical encoding of color predicts enhanced McCollough effects in anomalous trichromats

Nonlinear encoding of chromatic contrast by the early visual cortex predicts that anomalous trichromats will show a larger McCollough effect than normal trichromats. In Experiment 1 we employed the McCollough effect to probe the cortical representation of saturation in normal trichromats, and used the results to predict enhanced McCollough effects for anomalous trichromats, which we measured in Experiment 2. In Experiment 1 three participants adapted to red and green orthogonal gratings of four different saturations. Using nulling to measure aftereffect strength, we found that halving the saturation of the inducing gratings decreased aftereffect strength only slightly, consistent with a compressive coding of saturation in early visual cortex. In anomalous trichromats, cone contrasts between red and green are greatly decreased from those of normal trichromats, but induced aftereffects are only slightly decreased, because of the non-linearity in the cortical encoding of saturation. To null the aftereffect, however, the retinal color deficiency must be overcome by adding more color to the null than required by normal trichromats. We confirmed this prediction in Experiment 2 where four anomalous trichromats required nulling stimuli approximately four times more saturated than did normal trichromats. We consider two competing models to explain our results: in a 'pigment swap' model anomalous trichromats have an altered photopigment but process color postreceptorally in the same way as normal trichromats; in a 'postreceptoral compensation' model the cortical representation of red-green contrasts is amplified to compensate for reduced cone contrasts. The latter provided a better fit to our data.

A simplified physiological model of rate-level functions of auditory-nerve fibers

Several approaches have been used to describe the rate-level functions of auditory-nerve fibers (ANFs). One approach uses descriptive models that can be fitted easily to data. Another derives rate-level functions from comprehensive physiological models of auditory peripheral processing. Here, we seek to identify the minimal set of components needed to provide a physiologically plausible account of rate-level functions. Our model consists of a first-order Boltzmann mechanoelectrical transducer function relating the instantaneous stimulus pressure to an instantaneous output, followed by a lowpass filter that eliminates the AC component, followed by an exponential synaptic transfer function relating the DC component to the mean spike rate. This is perhaps the simplest physiologically plausible model capable of accounting for rate-level functions under the assumption that the model parameters for a given ANF and stimulus frequency are level-independent. We find that the model typically accounts well for rate-level functions from cat ANFs for all stimulus frequencies. More complicated model variants having saturating synaptic transfer functions do not perform significantly better, implying the system operates far away from synaptic saturation. Rate saturation in the model is caused by saturation of the DC component of the filter output (e.g., the receptor potential), which in turn is due to the saturation of the transducer function. The maximum mean spike rate is approximately constant across ANFs, such that the slope parameter of the exponential synaptic transfer function decreases with increasing spontaneous rate. If the synaptic parameters for a given ANF are assumed to be constant across stimulus frequencies, then frequency- and level-dependent input nonlinearities are derived that are qualitatively similar to those reported in the literature. Contrary to assumptions in the literature, such nonlinearities are obtained even for ANFs having high spontaneous rates. Finally, spike-rate adaptation is examined and found to be accounted for by a decrease in the slope parameter of the synaptic transfer function over time following stimulus onset.

An improved model for the rate-level functions of auditory-nerve fibers

Acoustic information is conveyed to the brain by the spike patterns in auditory-nerve fibers (ANFs). In mammals, each ANF is excited via a single ribbon synapse in a single inner hair cell (IHC), and the spike patterns therefore also provide valuable information about those intriguing synapses. Here we reexamine and model a key property of ANFs, the dependence of their spike rates on the sound pressure level of acoustic stimuli (rate-level functions). We build upon the seminal model of Sachs and Abbas (1974), which provides good fits to experimental data but has limited utility for defining physiological mechanisms. We present an improved, physiologically plausible model according to which the spike rate follows a Hill equation and spontaneous activity and its experimentally observed tight correlation with ANF sensitivity are emergent properties. We apply it to 156 cat ANF rate-level functions using frequencies where the mechanics are linear and find that a single Hill coefficient of 3 can account for the population of functions. We also demonstrate a tight correspondence between ANF rate-level functions and the Ca(2+) dependence of exocytosis from IHCs, and derive estimates of the effective intracellular Ca(2+) concentrations at the individual active zones of IHCs. We argue that the Hill coefficient might reflect the intrinsic, biochemical Ca(2+) cooperativity of the Ca(2+) sensor involved in exocytosis from the IHC. The model also links ANF properties with properties of psychophysical absolute thresholds.

Auditory signal detection appears to depend on temporal integration of subthreshold activity in auditory cortex

The threshold of hearing decreases with increasing sound duration up to a limit of a few hundred milliseconds, whereas other auditory time constants are orders of magnitude shorter. A possible solution to this resolution-integration paradox is that temporal integration occurs more centrally than computations depending on high temporal resolution. But this would require information about subthreshold events in the periphery to reach higher centers. Here we show that this prerequisite is fulfilled. The auditory evoked response to a just perceptible pulse series does basically not depend on whether single pulses are below or above behavioral threshold. The failure to find evidence of temporal integration up to response latencies of 30 ms suggests that the integrator is located more centrally than primary auditory cortex. By using noise to its advantage, the auditory system apparently has established a central integration mechanism that is about as efficient as the peripheral one in the visual system.

Auditory brainstem response at the detection limit

Specific predictions regarding the level dependence of auditory evoked responses near the detection limit were made in a companion modeling study (Lütkenhöner, J Assoc Res Otolaryngol 9:102-121, 2008). Here, these predictions are experimentally tested for auditory brainstem responses (ABR) to Gaussian-shaped 4-kHz tone pulses (full width at half maximum = 0.5 ms) that were presented at sound levels close to the subjective threshold. In the average of over about one million stimulus repetitions (repetition period = 16 ms), the amplitude of ABR wave V showed a smooth transition from a proportional to a logarithmic growth with increasing sound intensity. The latter type of growth corresponds to a linear increase with respect to sound level measured in decibels. Alternatively, the ABR amplitude near the detection limit may be considered a linear function of sound pressure, although-according to the model-this is only an approximation. Data and model are consistent with the view that a sensory threshold does not exist for the auditory modality, in accordance with signal detection theory. Even so, the model may be used to define a quasithreshold that is comparable to the subjective threshold.